Question

Consider the line that passes through the point (3, -6) and has a slope of 4.

Part 1: Write the equation of this line using point-slope form.
Part 2: Using your equation from part 1, rewrite this equation in slope-intercept form. Make sure to show all of your work.
Part 3: Using your equation from part 2, rewrite this equation in standard form. Make sure to show all of your work.

Answer 1

When you show the work can you put it all in one reply. It's easier for me. please.

Answer 2

ok here we go

Part 1
once again you are given a point and a slope right? so to find the equation of the line you need to use the "point-slope" formula, because that is the information you have

the point - slope formula is \(y-y_1=m(x-x_1)\)
you directly substitute the numbers you are given for \(x_1,y_1,m\) in this case they are \(x_1=3,y_1=-6,m=4\) so you write \[y-(-6)=4(x-3)\] or
\[y+6=4(x-3)\]

end of Part 1

Answer 3

Part 2

rewrite \(y+6=4(x-3)\) in the slope - intercept form. the slope intercept form in general is \(y=mx+b\) so we need to solve for \(y\)
steps are
1) multiply out on the right using the distributive law
\[y+6=4(x-3)\]
\[y+6=4x-12\]
2) subtract 6 from both sides
\[y=4x-12\]
end of Part 2

Answer 4

part 3
rewrite in standard form. standard form is \(ax+by=c\) to this end we use algebra to put the \(x\) and \(y\) terms on one side of the equal sign
\[y=4x-18\]
\[-4x+y=-18\] or if you prefer, multiply both sides by \(-1\) and write
\[4x-y=18\]

end of part 3

Answer 5

Thank you SO SO SO much.

Answer 6

that is correct, no step is missing.

in your first post you were given two incorrect answers. one was that the "slope - intercept" form was \(y-y_1=m(x-x_1)\) which is incorrect. the other was that the answer was \(y=4x-6\) which was also incorrect

Answer 7

yw

Answer 8

SO part three would look like this
y=4x−18
multiply both sides by -1
4x−y=18

Answer 9

not quite. to write in "standard form" you need to change
\[y=mx+b\] to
\[ax+by=c\] in other words put the variables on one side of the equal sign and the constant on the other

Answer 10

So it would just be 4x−y=18

Answer 11

part 3
\[y=4x-18\] subtract \(4x\) from both sides get
\[-4x+y=-18\] multiply both sides by \(-1\) get
\[4x-y=18\]

those are the steps

Answer 12

yup, that is it
\[4x-y=18\]

Answer 13

you got this now, more or less? we can do another if you like

Answer 14

I think I got it.
Thanks again (:
Can you help me with a graph?

Answer 15

I posted it.